Answer to Question #120002 in Statistics and Probability for Bernard

Question

(2a). According to the Ministry of Health, the height of Guinean travellers who were quarantined in Tamale
for the novel coronavirus were normally distributed about a mean of 160cm and a standard deviation
of 8cm. Find the probability that a traveller selected at random has

i) Height between 148cm and 175cm
ii) Height above 164cm
iii) Height below 179cm

Answer 1

a) Height between 148 cm and 175 cm 

$Z(x =148 ) +Z(x=175)= Z(\frac{148-160}{8})+Z(\frac{175-160}{8}) = Z(-1.5)+Z(1.87)=0.06681+0.96926=1.036$

b) Height above 164 cm  

$=0.5-Z(x =164) = 0.5-Z(\frac{164-160}{8})=0.5-Z(0.5) = 0.5-0.69146= -0.19146$

c) Height below 179 cm

$Z(x = 179) = Z(\frac{179-160}{8})= Z(2.375) =$ 0.99111